Coulomb's law (6.2.2)
On this page
Coulomb’s law states that any two point charges exert electrostatic forces on one another that are directly proportional to the product of their charges, and inversely proportional to the square of the distance between them.
Where:
- is the electrostatic force,
- and is the charge of each respective point charge, and
- is the separation distance.
Coulomb’s law applies to point charges, but can be valid for extended objects such as spheres. Spheres must be spherically symmetric, and the distance between the centres of two spheres must be much greater than their radii: essentially modelling them as point charges.
Coulomb’s law also only applies for stationary charges. If the charges are moving, then this introduces additional magnetic forces.
The law also assumes there are no external electric fields or other forces influencing the charges. If external fields are present, the resultant force must account for these additional interactions.
The diagram below shows the direction of the electrostatic forces between two point charges that have opposite charge and like charge:
Both charges in each case experience the same force due to Newton’s third law, which states that the charges will exert equal and opposite forces on one another.
Coulomb’s law states that the force between two point charges with charges and , separated by a distance is given by the equation:
Where:
- is the electrostatic force,
- and is the charge of each respective point charge, and
- is the separation distance.
- The constant of proportionality is the Boltzmann constant.
In Coulomb’s law, the constant of proportionality that is the Boltzmann constant, may be written in terms of the permittivity of free space . This allows one to rewrite Coulomb’s law as:
The permittivity of free space is a fundamental physical constant. It characterises the ability of an electric field to form and propagate throughout a vacuum, and how the electric fields interact. A greater value for the permittivity of free space would mean a weaker electric field for the same charges and distances.
Question walkthrough
Separation of Two Repelling Point Charges
Calculates the separation between two repelling point charges given their charge magnitudes and the force between them, using Coulomb's law.
A point charge or charged metal sphere produces a radial electric field. Field lines become less dense with increasing distance from the source, meaning the strength of the field decreases with distance from the charge.
The electric field strength at a distance from the centre of the sphere is equal to the electrostatic force divided by the charge. One can substitute Coulomb’s law for the force to obtain:
The electric field strength is directly proportional to the charge and is inversely proportional to the square of the distance , i.e. the strength decreases with distance.
The electric field for a charged metal sphere and a point charge decreases with distance.
The electric field strength is inversely proportional to the square of the distance from the centre. Therefore, if we plot the electric field strength against the reciprocal of the square of the distance from the centre we obtain a linear relationship:
As can be seen, the gradient is constant as it is a straight line relationship, and is proportional to the charge Therefore, one could obtain the magnitude of the charge from a plot of against
Question walkthrough
Electric Field Strength from a Point Charge
Calculates the electric field strength at a given distance from a point charge using Coulomb's law.
There are many similarities and differences between electric fields and gravitational fields. Both point charges and point masses produce radial fields, and objects with charge and mass are acted upon by a force within the electric and gravitational field, respectively.
The table below summarises the key similarities and differences between electric fields and gravitational fields for point charges and point masses:
A field is a region in space where a force can be exerted on objects possessing certain properties (such as charge or mass) without physical contact.
Fields are used to explain how forces can act at a distance, allowing one object to exert influence on another across space.
Electric fields are one of several forms of fields within physics that give rise to a force. There are many similarities and differences between different types of fields, such as electric fields, gravitational fields and magnetic fields.
All three follow the same principles that define fields, but have differences in the objects they act upon:
- Electric fields Charged objects
- Gravitational fields Objects with mass
- Magnetic fields Charged objects in motion and objects with magnetic poles
- Electromagnetic fields Combination of electric and magnetic fields.